Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions

Abstract

The Barut-Girardello coherent states (BG CS) representation is extended to the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson realizations. The sp(N,R) BG CS take the form of multimode ordinary Schrödinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode Hilbert space and the relation between the canonical CS and the u(p,q) BG-type CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and their discrete superpositions contain many states studied in quantum optics (even and odd N-mode CS, pair CS) and provide an approach to quadrature squeezing, alternative to that of intelligent states. New subsets of weakly and strongly nonclassical states are pointed out and their statistical properties (first- and second-order squeezing, photon number distributions) are discussed. For specific values of the angle parameters and small amplitude of the canonical CS components these states approaches multimode Fock states with one, two or three bosons/photons. It is shown that eigenstates of a squared non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of the quadratures of A.

29 pages, LaTex, 5 figures. Improvements in text, corrections in some formulas. To appear in J. Phys. A, v. 31

References in corpus (9)

• Preparation of Nonclassical States in Cavities with a Moving Mirror
• SU(2) and SU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states
• Robertson Intelligent States
• Generation of single-mode SU(1,1) intelligent states and an analytic approach to their quantum statistical properties
• On the squeezed states for n observables
• Necessary and Sufficient Classicality Conditions on Photon Number Distributions
• Extension of the Barut-Girardello Coherent State and Path Integral
• Extension of the Barut-Girardello Coherent State and Path Integral II
• Higher power squeezed states, Jacobi matrices, and the Hamburger moment problem

Cited by in corpus (6)

• Introduction to Coherent States and Quantum Information Theory
• Quantization of the Optical Phase Space S^2 = {phi mod 2pi, I > 0} in Terms of the Group SO(1,2)
• Generalized uncertainty relations and coherent and squeezed states
• Nonclassical properties and quantum resources of hierarchical photonic superposition states
• The Uncertainty Way of Generalization of Coherent States
• Geometry of Generalized Coherent States : Some Calculations of Chern Characters